My post above depended on the Washington Post article which is not such a great source. I learned from another blogger (at Open Left) that the Financial Times reported Obama's remarks more fully:

"The outline for a durable ceasefire is clear: Hamas must end its rocket fire: Israel will complete the withdrawal of its forces from Gaza: the US and our partners will support a credible anti-smuggling and interdiction regime, so that Hamas cannot re-arm," the US president said.

"As part of a lasting ceasefire, Gaza's border crossings should be open to allow the flow of aid and commerce, with an appropriate monitoring regime, with the international and Palestinian Authority participating."

Certainly this is a lot better than what I had originally thought.